scholarly journals On the quaternionic manifolds whose twistor spaces are Fano manifolds

2015 ◽  
Vol 67 (4) ◽  
pp. 507-511
Author(s):  
Radu Pantilie
Keyword(s):  
Fano Manifolds ◽  
Twistor Spaces ◽  
Quaternionic Manifolds

scholarly journals Quaternionic-like manifolds and homogeneous twistor spaces

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160598
Author(s):  
Radu Pantilie
Keyword(s):  
Complex Manifolds ◽  
Twistor Spaces ◽  
Adequate Level ◽  
Homogeneous Complex ◽  
Quaternionic Manifold ◽  
Quaternionic Geometry ◽  
Real Analytic ◽  
Quaternionic Manifolds

Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the ‘quaternionic-like manifolds’. These contain, as particular subclasses, the CR quaternionic and the ρ -quaternionic manifolds. Moreover, the notion of ‘heaven space’ finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ -quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals Gauging the Heisenberg algebra of special quaternionic manifolds

2005 ◽  
Vol 610 (1-2) ◽  
pp. 147-151 ◽  
Author(s):  
R. D'Auria ◽  
S. Ferrara ◽  
M. Trigiante ◽  
S. Vaulà
Keyword(s):  
Heisenberg Algebra ◽  
Quaternionic Manifolds

Estimation of Ricci tensor on certain Fano manifolds

2000 ◽  
Vol 233 (3) ◽  
pp. 481-505 ◽  
Author(s):  
Adnène Ben Abdesselem ◽  
Pascal Cherrier
Keyword(s):  
Ricci Tensor ◽  
Fano Manifolds

Double Covers of Some Fano Manifolds as Hyperplane Sections

1998 ◽  
Vol 193 (1) ◽  
pp. 93-110
Author(s):  
Antonio Lanteri ◽  
Gianluca Occhetta
Keyword(s):  
Fano Manifolds ◽  
Double Covers ◽  
Hyperplane Sections
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